Broadband and wide viewing angle waveplate having pi-cell

ABSTRACT

An optical waveplate is provided. The optical waveplate includes a positive-C film including a first liquid crystal (“LC”) layer. Tilt angles of LC molecules vary along a thickness direction of the first LC layer. The optical wave also includes an LC cell disposed at a first side of the positive-C film and including a second LC layer aligned in an optically compensated bend (“OCB”) mode. The optical waveplate also includes a positive-A film disposed at a second side of the positive-C film. The optical waveplate further includes a negative biaxial retardation film disposed between the positive-A film and the positive-C film. The LC cell is switchable between at least two predetermined states.

CROSS REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application No.62/833,410, filed on Apr. 12, 2019, which is incorporated by referencein its entirety.

BACKGROUND

Waveplates have been implemented in many instruments and optical systemsfor polarization control. A waveplate controls the polarization byretarding (or delaying) a component of polarization (or a polarizationcomponent) with respect to an orthogonal component. Retardance is aphase shift (hence “retardance” may also be referred to as “phaseretardance”) between the polarization component projected along a fastaxis and the orthogonal component projected along a slow axis.Waveplates utilizing tunable birefringent materials, e.g., liquidcrystal (“LC”) waveplates, have the advantage of non-mechanically tuningof the retardance.

SUMMARY

One aspect of the present disclosure provides an optical waveplate. Theoptical waveplate includes a positive-C film including a first liquidcrystal (“LC”) layer. Tilt angles of LC molecules in the first LC layervary along a thickness direction of the first LC layer. The opticalwaveplate also includes an LC cell disposed at a first side of thepositive-C film and including a second LC layer aligned in an opticallycompensated bend (“OCB”) mode. The optical waveplate also includes apositive-A film disposed at a second side of the positive-C film. Theoptical waveplate further includes a negative biaxial retardation filmdisposed between the positive-A film and the positive-C film. The LCcell is switchable between at least two predetermined states.

Other aspects of the present disclosure can be understood by thoseskilled in the art in light of the description, the claims, and thedrawings of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The following drawings are provided for illustrative purposes accordingto various disclosed embodiments and are not intended to limit the scopeof the present disclosure. In the drawings:

FIG. 1 illustrates a schematic diagram of an optical waveplate accordingto an embodiment of the present disclosure;

FIG. 2 illustrates a schematic cross-sectional view of a Pi-cell in asplay state according to an embodiment of the present disclosure;

FIG. 3 illustrates a schematic cross-sectional view of a Pi-cell in abend state according to an embodiment of the present disclosure;

FIG. 4 illustrates a schematic cross-sectional view of a Pi-cell in ahomeotropic state according to an embodiment of the present disclosure;

FIG. 5 illustrates refractive indices of a retardation film according toan embodiment of the present disclosure;

FIG. 6 illustrates a schematic diagram of film orientations in anoptical waveplate according to an embodiment of the present disclosure;

FIG. 7A illustrates a schematic diagram of a positive-C film accordingto an embodiment of the present disclosure;

FIG. 7B illustrates tilt angles of liquid crystal (“LC”) molecules in apositive-C film according to an embodiment of the present disclosure;

FIG. 8 illustrates simulation results regarding broadband performance ofan optical waveplate according to an embodiment of the presentdisclosure;

FIG. 9 illustrates simulation results regarding large viewing angleperformance of the optical waveplate according to an embodiment of thepresent disclosure;

FIG. 10 illustrates simulation results regarding Stokes parameter S3 ofan output light versus incident angles when no electric field is appliedto the optical waveplate, according to an embodiment of the presentdisclosure;

FIG. 11 illustrates simulation results regarding Stokes parameter S3 forof an output light versus incident angles when an electric field isapplied to the optical waveplate, according to an embodiment of thepresent disclosure;

FIG. 12 illustrates a perspective view of a near-eye display (“NED”)according to an embodiment of the present disclosure;

FIG. 13 illustrates a cross section of a front body of the NED shown inFIG. 12; and

FIG. 14 illustrates a schematic diagram of a varifocal block accordingto an embodiment of the present disclosure.

DETAILED DESCRIPTION

Embodiments consistent with the present disclosure will be describedwith reference to the accompanying drawings, which are merely examplesfor illustrative purposes and are not intended to limit the scope of thepresent disclosure. Wherever possible, the same reference numbers areused throughout the drawings to refer to the same or similar parts, anda detailed description thereof may be omitted.

Further, in the present disclosure, the disclosed embodiments and thefeatures of the disclosed embodiments may be combined. The describedembodiments are some but not all of the embodiments of the presentdisclosure. Based on the disclosed embodiments, persons of ordinaryskill in the art may derive other embodiments consistent with thepresent disclosure. For example, modifications, adaptations,substitutions, additions, or other variations may be made based on thedisclosed embodiments. Such variations of the disclosed embodiments arestill within the scope of the present disclosure. Accordingly, thepresent disclosure is not limited to the disclosed embodiments. Instead,the scope of the present disclosure is defined by the appended claim.

As used herein, the terms “couple,” “coupled,” “coupling,” or the likemay encompass an optical coupling, a mechanical coupling, an electricalcoupling, an electromagnetic coupling, or a combination thereof. An“optical coupling” between two optical elements refers to aconfiguration in which the two optical elements are arranged in anoptical series, and a light output from one optical element may bedirectly or indirectly received by the other optical element. An opticalseries refers to optical positioning of a plurality of optical elementsin a light path, such that a light output from one optical element maybe transmitted, reflected, diffracted, converted, modified, or otherwiseprocessed or manipulated by one or more of other optical elements. Insome embodiments, the sequence in which the plurality of opticalelements are arranged may or may not affect an overall output of theplurality of optical elements. A coupling may be a direct coupling or anindirect coupling (e.g., coupling through an intermediate element).

The phrase “at least one of A or B” may encompass all combinations of Aand B, such as A only, B only, or A and B. Likewise, the phrase “atleast one of A, B, or C” may encompass all combinations of A, B, and C,such as A only, B only, C only, A and B, A and C, B and C, or A and Band C. The phrase “A and/or B” may be interpreted in a manner similar tothat of the phrase “at least one of A or B.” For example, the phrase “Aand/or B” may encompass all combinations of A and B, such as A only, Bonly, or A and B. Likewise, the phrase “A, B, and/or C” has a meaningsimilar to that of the phrase “at least one of A, B, or C.” For example,the phrase “A, B, and/or C” may encompass all combinations of A, B, andC, such as A only, B only, C only, A and B, A and C, B and C, or A and Band C.

When a first element is described as “attached,” “provided,” “formed,”“affixed,” “mounted,” “secured,” “connected,” “bonded,” “recorded,” or“disposed,” to, on, at, or at least partially in a second element, thefirst element may be “attached,” “provided,” “formed,” “affixed,”“mounted,” “secured,” “connected,” “bonded,” “recorded,” or “disposed,”to, on, at, or at least partially in the second element using anysuitable mechanical or non-mechanical manner, such as depositing,coating, etching, bonding, gluing, screwing, press-fitting,snap-fitting, clamping, etc. In addition, the first element may be indirect contact with the second element, or there may be an intermediateelement between the first element and the second element. The firstelement may be disposed at any suitable side of the second element, suchas left, right, front, back, top, or bottom.

When the first element is shown or described as being disposed orarranged “on” the second element, term “on” is merely used to indicatean example relative orientation between the first element and the secondelement. The description may be based on a reference coordinate systemshown in a figure, or may be based on a current view or exampleconfiguration shown in a figure. For example, when a view shown in afigure is described, the first element may be described as beingdisposed “on” the second element. It is understood that the term “on”may not necessarily imply that the first element is over the secondelement in the vertical, gravitational direction. For example, when theassembly of the first element and the second element is turned 180degrees, the first element may be “under” the second element (or thesecond element may be “on” the first element). Thus, it is understoodthat when a figure shows that the first element is “on” the secondelement, the configuration is merely an illustrative example. The firstelement may be disposed or arranged at any suitable orientation relativeto the second element (e.g., over or above the second element, below orunder the second element, left to the second element, right to thesecond element, behind the second element, in front of the secondelement, etc.).

The wavelength ranges, spectra, or bands mentioned in the presentdisclosure are for illustrative purposes. The disclosed optical device,system, element, assembly, and method may be applied to a visiblewavelength range, as well as other wavelength ranges, such as anultraviolet (“UV”) wavelength range, an infrared wavelength range, or acombination thereof.

For polarimetric imaging systems, it is highly desirable that LCwaveplates have broadband performance to cover wavelengths ranging fromvisible (“VIS”) to near infrared (“NIR”) regions, a large acceptanceangle (i.e., large incident angle), a low residual retardance, a fastresponse, and a capability of being switched between different states,for example, between a substantially zero retardance and a non-zeroretardance value (e.g. half-wave retardance, quarter-wave retardance).It may be a challenge to obtain the above-mentioned advantages in LCwaveplates using twisted nematic liquid crystal (“TNLC”) cells at thesame time. For example, the response time of a typical nematic LCwaveplate is about 5 milliseconds (“ms”), and the residual retardance islarge because nematic LC molecules may not be completely reorientedalong an external electric field. Compared to TNLC cells, an LC cellincluding an LC layer aligned in an optically compensated bend (“OCB”)mode, also referred to as a Pi-cell, exhibits fast switching speed(about 2 ms) and naturally wide viewing angles due to a parallelalignment of LC molecules. In addition, a high contrast may be achievedwith a compensation film to subtract residual birefringence at substratesurfaces. Thus, Pi-cells may be used to form broadband LC waveplateswith a fast response and a wide viewing angle.

The present disclosure provides an optical waveplate having broadbandperformance that covers wavelengths ranging from visible (“VIS”) to nearinfrared (“NIR”) regions, a large acceptance angle (e.g., suitable for alarge incident angle), a low residual retardance, a fast response, and acapability of being switchable between states of different phaseretardances, such as between a substantially zero retardance (or anequivalent full-wave retardance, e.g., one full-wave retardance, twofull-wave retardance, etc.) and a non-zero fractional-wave retardance(e.g. half-wave retardance, quarter-wave retardance). The opticalwaveplate may include a liquid crystal (“LC”) cell including a nematicLC layer aligned in an optically compensated bend (“OCB”) mode, apositive-C film, a negative biaxial retardation film, and a positive-Afilm arranged in an optical series. The LC cell may be controllable byan external electric field to switch between at least two predeterminedstates, which include a splay state and a homeotropic state. In someembodiments, the LC cell and the positive-A film may be disposed at twoopposite sides of the positive-C film, and the negative biaxialretardation film may be disposed between the positive-A film and thepositive-C film.

In some embodiments, when the optical waveplate provides a non-zerofractional-wave phase retardance, the optical waveplate may beconfigured to rotate a polarization of a broadband light (e.g., apolychromatic light) over a range of wavelengths and/or a range ofincident angles. An amount of the non-zero fractional-wave phaseretardance provided by the optical waveplate may be substantiallywavelength independent over the range of wavelengths and/orsubstantially incident angle independent over the range of incidentangles. In some embodiments, the optical waveplate may be configured toperform a polarization conversion from a first polarization to a secondpolarization for the broadband light (e.g., a polychromatic light) overthe range of wavelengths and/or the range of incident angles. In someembodiments, when the optical waveplate provides a substantially zeroretardance (or an equivalent full-wave retardance, e.g., one full-waveretardance, two full-wave retardance, etc.), the optical waveplate maybe configured to substantially maintain a polarization of the broadbandlight (e.g., a polychromatic light) over the range of wavelengths and/orthe range of incident angles.

FIG. 1 illustrates a schematic diagram of an optical waveplate 100according to an embodiment of the present disclosure. The opticalwaveplate 100 may include a plurality of optical components arranged inan optical series. For illustrative purposes, FIG. 1 shows that theoptical waveplate 100 includes four optical components 101, 102, 103,and 104. In some embodiments, the optical waveplate 100 may include anysuitable number (e.g., two, three, five, six, etc.) of opticalcomponents. Each optical component may have a specific optical property.When combined, the four optical components may render desirable opticalproperties for the optical waveplate 100. For example, the opticalwaveplate 100 may be configured to provide an amount of phase retardanceto a broadband light (e.g., a polychromatic light) over a range ofwavelengths and/or over a range of incident angles. The four opticalcomponents may be oriented relative to each other, such that the amountof phase retardance provided by the optical waveplate 100 to thebroadband light may be substantially wavelength independent (orindependent of the wavelength) over the range of wavelengths and/orsubstantially independent of the incident angle (or incident angleindependent) over the range of the incident angles. In some embodiments,when the optical waveplate 100 provides a non-zero fractional-wave phaseretardance, the optical waveplate 100 may be configured to perform apolarization conversion from a first polarization to a secondpolarization for broadband light (e.g., a polychromatic light) over therange of wavelengths and/or the range of incident angles. In someembodiments, when the optical waveplate 100 provides a substantiallyzero retardance (or an equivalent full-wave retardance, e.g., onefull-wave retardance, two full-wave retardance, etc.), the opticalwaveplate 100 may be configured to substantially maintain a polarizationof the broadband light (e.g., a polychromatic light) over the range ofwavelengths and/or the range of incident angles.

In some embodiments, the optical waveplate 100 may include an LC celland a plurality of compensation films arranged in an optical series. TheLC cell may include a nematic LC layer aligned in an OCB mode, where thenematic LC molecules near or adjacent the upper and lower substrates maybe aligned in a parallel direction. In some embodiments, thecompensation films may include one or more positive-C films, one or morepositive-A films, and/or one or more negative biaxial retardation films.As used herein, the term “film” may encompass film, plate, layer, etc.,and can be any suitable thickness. The compensation films are opticalfilms that may compensate for wavelength dispersion and an axial phasedifference so as to overcome a restricted viewing angle caused by theparallel alignment of the nematic LC molecules at the boundaries of theLC cell. The compensation films may be optically transmissive (e.g.,substantially transparent) for lights in the visible band (about 380 nmto about 700 nm), and in a portion of the infrared (“IR”) band (about700 nm to about 1 mm). In some embodiments, a retardation film may be afilm including polymerized or crosslinked LC materials. For example, theretardation film may be obtained by disposing a layer of polymerizableLC material precursors on a substrate, polymerizing the LC materialsthat are homogeneously or homeotropically aligned in an LC phase (e.g.,photo-polymerizing by exposure to a linear polarized light, orthermal-polymerizing by exposure to a predetermined temperature), andoptionally removing the polymerized material from the substrate.

In some embodiments, the LC cell may be an active component in theoptical waveplate 100, and other components included in the opticalwaveplate 100 may be passive. The term “active” means that the opticalproperty (e.g., retardance) of the LC cell may be variable or switchableby an external field (e.g., an electric field, a magnetic field, or alight field) applied to the LC cell. In some embodiments, thecompensation films may be passive components. In other words, noexternal field is applied to the compensation films to change or switchthe optical properties of the compensation films. For example, the LCcell that is an active component may provide a variable phase retardanceunder different driving voltages, while a compensation film that is apassive element may provide a constant phase retardance. Throughadjusting the driving voltage applied to the LC cell, the opticalwaveplate 100 may be configured to provide various phase retardances fora predetermined spectrum, such as λ/4 (90°) retardance, λ/2 (180°)retardance, λ (360°) retardance, where λ is a predetermined wavelength.By switching the driving voltage applied to the LC cell, the opticalwaveplate 100 may be switchable between states of different phaseretardances.

The compensation films and the LC cell may be arranged in a suitableconfiguration to achieve desirable optical properties of the opticalwaveplate 100. In one embodiment, as shown in FIG. 1, the opticalcomponent 101 may be the positive-A film, the optical component 102 maybe the negative biaxial retardation film, the optical component 103 maybe the positive-C film, and the optical component 104 may be the LC cellhaving the LC layer aligned in the OCB mode. That is, the positive-Cfilm 103 may be disposed at a side of the LC cell 104. The positive-Cfilm 103 may have a first side facing the LC cell 104 and an opposingsecond side, and the negative biaxial retardation film 102 may bedisposed at the second side of the positive-C film 103. The negativebiaxial retardation film 102 may have a first side facing the positive-Cfilm 103 and an opposing second side, and the positive-A film 101 may bedisposed at the second side of the negative biaxial retardation film102.

The stack configuration of the four optical components shown in FIG. 1is for illustration only. Other suitable arrangements may also be used.In addition, in some embodiments, any other combinations of any numberof optical components may be used. For example, in some embodiments, theoptical waveplate 100 may include one layer, two layers, three layers,five layers, six layers, etc. In some embodiments, the four layers shownin FIG. 1 may be arranged in another order or sequence.

FIG. 2 illustrates a schematic cross-sectional view of an LC cell 200according to an embodiment of the present disclosure. The LC cell 200may be an embodiment of the LC cell 104 included in the opticalwaveplate 100, as shown in FIG. 1. As shown in FIG. 2, the LC cell 200may include upper and lower substrates 202 arranged opposite to eachother, e.g., a top substrate and a bottom substrate. The substrates 202may be at least partially optically transmissive (e.g., substantiallytransparent) to lights in the visible band (about 380 nm to about 700nm). In some embodiments, the substrates 202 may also be at leastpartially optically transmissive (e.g., substantially transparent) to ina portion of the infrared (“IR”) band (about 700 nm to about 1 mm). Thesubstrates 202 may include a suitable material that is at leastpartially optically transmissive (e.g., substantially transparent) tolights in above-listed wavelengths range, e.g., SiO₂, plastic, sapphire,etc. The substrate 202 may be rigid, semi-rigid, flexible, orsemi-flexible. In some embodiments, the substrate 202 may be a part ofanother optical device or another optoelectrical device. For example,the substrate 202 may be a part of a functional device, such as adisplay screen. In some embodiments, the substrate 202 may be a part ofan optical lens assembly, such as a lens substrate of the optical lensassembly. Electrodes 204 may be disposed on opposing surfaces of thesubstrates 202 and may be configured to apply an electric field. In someembodiments, the electrodes 204 may be indium tin oxide (“ITO”)electrodes.

The LC cell 200 may include at least one alignment layer 206 configuredto at least partially align the LC molecules included in the LC cell200. In the embodiment shown in FIG. 2, two alignment layers 206 aredisposed on opposing surfaces of the electrodes 204. In someembodiments, one of the alignment layers 206 may be omitted. In someembodiments, both of the alignment layers 206 may be omitted. In suchembodiments, the alignment of the LC molecules included in the LC cell200 may be introduced in the LC molecules through bulk alignment using,e.g., an external electric field, an external light field, or anexternal magnetic field, etc. The LC cell 200 may also include an LClayer 208 may be sandwiched between the two alignment layers 206. The LClayer 208 may include nematic LC molecules 210. The two alignment layers206 may be configured with a homogeneous parallel alignment direction,for example, in a x-direction indicated by an arrow 212, through whichthe LC layer 208 may be aligned in the OCB mode. That is, the nematic LCmolecules 210 adjacent or near the upper and lower substrates 202 may beoriented in a parallel direction.

The LC cell 200 may be referred to as a Pi-cell. The name Pi-cell comesfrom the twist of directors of LC molecules, which is 180° formed by theparallel alignment direction (e.g., parallel rubbing direction) on eachsubstrate. As a comparison, in a TNLC cell, the alignment directions ontwo substrates are perpendicular to each other. Thus, a 90° twist of LCdirectors from one substrate to the other is formed inside the TNLCcell. Further, in the Pi-cell, nematic LC molecules 210 adjacent or nearthe upper and lower substrates 202 may be aligned uniformly along apredetermined pre-tilt angle θ and a pre-twisted angle φ, allowing theLC molecules 210 to maintain a slight inclination in a predetermineddirection when an external voltage is not applied between the substrates202. The pre-tilt angle θ is defined as an angle between the long axisof the LC molecule 210 and the substrate 202.

FIGS. 2-4 illustrate a switching process of the LC cell 200 by anexternal electric field. In a voltage-off state (e.g., V₀=0V, or moregenerally, or more generally below a threshold voltage of the LC cell200), as shown in FIG. 2, the LC cell 200 may be in a splay state inwhich the LC molecules 210 are elastically deformed at a splayconfiguration because of surface constraints. Thus, the LC molecules 210may be oriented parallel to the alignment directions 212 of bothalignment layers 206. For example, the LC molecules 210 at the middleportion of the LC layer 208 are parallel to the alignment directions212, and the LC molecules 210 at other portions between the middleportion and the substrates alignment layers 206 are substantiallyparallel to the alignment directions 212 with small pretilt angles(e.g., 0°-10°, etc.).

In a voltage-on state, when a relatively low electric field is applied(e.g., when a relatively low voltage V₁ (e.g., V₁=2V) is applied) to theLC cell 200, as shown in FIG. 3, the LC cell 200 may be switched to abend state, in which the LC molecules 210 at the middle portion of theLC layer 208 are reoriented by the electric field E to be perpendicularto the substrates 202, while other LC molecules 210 between the middleportion and the alignment layers 206 are still oriented substantiallyparallel to the alignment directions 212 because of the surfaceconstraints of the alignment layers 206. When a relatively high electricfield is applied (e.g., when a relatively high voltage V₂ (e.g., V₂=10V)to the LC cell 200, as shown in FIG. 4, the LC cell 200 may be switchedto a homeotropic state, in which the majority of the LC molecules 210are reoriented by the electric field E to be perpendicular to thesubstrates 202 (except for the LC molecules 210 near (e.g., in directcontact with) the alignment layers 206). To obtain the bend state of theLC cell 200, an electric field greater than a predeterminedsplay-to-bend transition electric field (e.g., voltage) may be applied.To obtain the homeotropic structure of the LC cell 200, an electricfield greater than a bend-to-homeotropic transition electric field(e.g., voltage) may be applied. The transition electric fields (e.g.,transition voltages) may be determined by the LC materials and thethickness of the LC layer 208.

Compared to other LC switching modes such as twisted nematic (“TN”),vertically aligned (“VA”) and in-plane-switching (“IPS”) modes, thePi-cell exhibits a fast switching speed because of the reduced backfloweffect. Moreover, the Pi-cell has an intrinsic wide viewing anglebecause of the self-compensated structure. As shown in FIG. 2, beam 1and beam 2 transmitted through the LC cell 200 in two oblique incidencedirections may experience the same retardation. The self-compensationnature may not be applicable to lights with incident angles out of thedirector plane. Furthermore, the on-axis contrast ratio (“CR”) may below due to the residual birefringence even at a relatively high voltage.Thus, it may be desirable to couple optical compensation films with theLC cell 200 to achieve a high CR and a wide viewing angle.

FIG. 5 illustrates refractive indices of a retardation film 500. Asshown in FIG. 5, n_(x) and n_(y) are principal refractive indices inorthogonal directions at a film plane (e.g., x-y plane in FIG. 5) andn_(z) is a principal refractive index in an out-of-plane verticaldirection (e.g., z-direction in FIG. 5), which is also referred to asthe refractive index in the film thickness direction. Depending on themagnitudes of the refractive indices, the characteristics and the typesof the retardation films may be determined.

A positive-A film is a retardation film where n_(x)>n_(y)=n_(z). Thein-plane retardance of the positive-A film is determined by thedifference between two refractive indices in the film plane as well asthe thickness of the film according to the following Equation (1):

R _(in) =d×(n _(x) −n _(y))  (1),

wherein d is the thickness of the film, and Δn_(xy)=n_(x)−n_(y) is thein-plane birefringence of the film. A positive-A film typically has itsoptical axis aligned parallel to the plane of the film. (e.g., x-yplane).

A positive-C film is a retardation film where n_(x)=n_(y)<n_(z). Thethickness-direction retardance of the positive-C film is determined bythe difference between an in-plane refractive index and athickness-direction refractive index as well as a thickness of the filmaccording to the following Equation (2):

R _(th) =d×(n _(z) −n _(y))  (2),

wherein d is the thickness of the film, and Δn_(zy)=n_(z)−n_(y) is theout-of-plane (or thickness direction) birefringence of the film. Thatis, the positive-C film is a retardation film having a substantiallyzero in-plane retardance and a positive thickness-direction retardance.The positive-C film typically has its optical axis aligned to beperpendicular to the plane of the film (e.g., x-y plane). The positive-Cfilm may include a nematic LC layer where the tilt angle θ of thenematic LC molecules varies along the thickness direction of the film,e.g., the tilt angle θ of the nematic LC molecules is a function of thefilm thickness. The tilt angle θ is defined as an angle between the longaxis or the director of the LC molecule and the film plane.

A negative biaxial retardation film is a retardation film wheren_(x)>n_(y)>n_(z). The negative biaxial retardation film has both anin-plane retardance R_(ib) and a thickness-direction retardance R_(tb),which are defined as follows:

R _(ib) =d×(n _(x) −n _(y))  (3),

R _(tb) =d×(n _(z) −n _(y))  (4),

wherein d is the thickness of the film, Δn_(xy)=n_(x)−n_(y) is thein-plane birefringence of the film, and Δn_(zy)=n_(z)−n_(y) is theout-of-plane (or thickness direction) birefringence of the film. Thatis, the negative biaxial retardation film may have a positive in-planeretardance and a negative thickness-direction retardance.

In the disclosed embodiments, the fast axis or slow axis of aretardation film may be oriented relative to the alignment direction ofthe LC cell to achieve predetermined optical properties of the opticalwaveplate. FIG. 6 illustrates a schematic diagram of film orientationsin an optical waveplate 600 according to an embodiment of the presentdisclosure. The optical waveplate 600 may be an embodiment of theoptical waveplate 100 shown in FIG. 1. In FIG. 6, the optical component101 (e.g., a positive-A film), the optical component 102 (e.g., anegative biaxial retardation film), the optical component 103 (e.g., apositive-C film), and the optical component 104 (e.g., an LC cell) aredisplayed in an exploded view for illustrative purposes. As shown inFIG. 6, an alignment direction 1041 of the LC cell 104 may be orientatedat about −35° to about −50° relative to a predetermined direction 1111(e.g., y-axis in FIG. 6). The alignment direction 1041 may be apreferential alignment direction of the LC molecules included in the LCcell 104 (or a macroscopic alignment direction of the LC cell 104). Afast axis 1031 of the positive-C film 103 may be orientated at about 35°to about 50° relative to the predetermined direction 1111. A slow axis1021 of the negative biaxial retardation film 102 may be orientated atabout −35° to about −50° relative to the predetermined direction 1111. Aslow axis 1011 of the positive-A film 101 may be orientated at about 35°to about 50° relative to the predetermined direction 1111. In someembodiments, the predetermined direction 1111 may be a polarizationdirection of a linearly polarized light incident onto the LC cell 104.

In one embodiment, as shown in FIG. 6, the alignment direction 1041 ofthe LC cell 104 may be orientated by about −45° relative to they-direction (an example of the predetermined direction 1111). The fastaxis 1031 of the positive-C film 103 may be orientated by about 45°relative to the y-direction. The slow axis 1021 of the negative biaxialretardation film 102 may be orientated by about −45° relative to they-direction. The slow axis 1011 of the positive-A film 101 may beorientated by about 45° relative to the y-direction.

In one embodiment, the LC cell 104 may include liquid crystal materialshaving the following properties: K33/K11=1.3437, K22/K11=0.5937, Δε=11,where K₁₁, K₂₂, and K₃₃ are splay, twist, and bend elastic constants ofthe liquid crystal materials. The LC cell 104 may have a pre-tilt angleof about 3°, a thickness of about 1.3 μm, and a birefringence (Δn) ofabout 0.18. The positive-A film 101 may have a pre-tilt angle of about3°, a thickness of about 1 μm, and an in-plane birefringence (Δn) ofabout 0.18. The negative biaxial retardation film 102 may have apre-tilt angle of about 90°, a thickness of about 1 μm, and anout-of-plane birefringence (Δn) of about −0.11.

The positive-C film 103 may have a thickness of about 2 μm and anout-of-plane birefringence (Δn) of about 0.18. An exemplary LCconfiguration 700 of the positive-C film 103 is shown in FIG. 7A, andthe relationship between the tilt angle and the film thickness of thepositive-C film 103 is shown in FIG. 7B. As shown in FIGS. 7A and 7B,the positive-C film 103 may include a nematic LC layer 710, where thetilt angle of the LC molecules 720 may vary along the thicknessdirection of the film. For example, the tilt angle of the LC molecules720 may gradually vary from about 3° to about 90° as the normalized filmthickness increases from about 0 to about 0.5, then abruptly increase toabout −90° when the normalized film thickness approaches 0.55, changefrom about −90° to about −75° in a relative slow speed as the normalizedfilm thickness increases from about 0.55 to about 0.85, and change fromabout −75° to about −3° in a relative fast speed as the normalized filmthickness increases from about 0.85 to about 1. That is, along thethickness direction of the nematic LC layer 710, the absolute values ofthe tilt angles of the LC molecules 720 in the nematic LC layer 710 maygradually increase from two edges to a center portion of the nematic LClayer 710, respectively.

The LC configuration 700 of the positive-C film 103 shown in FIG. 7A isfor illustrative purposes, and is not intended to limit the scope of thepresent discourse. The LC configuration 700 of the positive-C film 103may be determined by various factors, such as the phase to be achieved,the compensation effect to be achieved, etc. In some embodiments, whenthe tilt angles of the LC molecules 720 gradually increase from each oftwo edges of the nematic LC layer 710 to the center portion of thenematic LC layer 710, the absolute values the tilt angles of the LCmolecules 720 at each of two edges of the nematic LC layer 710 may be ina range of about 0° to 5° (e.g., 1° to 3°), and the absolute values thetilt angles of the LC molecules 720 at the center portion of the nematicLC layer 710 may be in a range of about 85° to 90° (e.g., 88° to) 90°.In some embodiments, the positive-C film includes an LC material with anegative dielectric anisotropy. In some embodiments, the positive-C filmincludes an LC material with a positive dielectric anisotropy.

In the following, simulation results of the optical properties of theoptical waveplate 600 are illustrated in FIGS. 8-11. FIG. 8 illustratessimulation results showing a relationship between a retardance of theoptical waveplate 600 and an incident wavelength (e.g., a wavelength ofan incident light). FIG. 9 illustrates simulation results showing arelationship between the retardance of the optical waveplate 600 and anincident angle. FIG. 10 illustrates the simulation results showing arelationship between the Stokes parameter S3 of the light transmittedthrough the optical waveplate 600 (i.e., output light) and the incidentangle of the light incident onto the optical waveplate 600 (i.e., inputlight) when the LC cell 104 is switched off to be in the splay state(V₀=0V). FIG. 11 illustrates the simulation results showing arelationship between the Stokes parameter S3 of the light transmittedthrough the optical waveplate 600 (i.e., output light) and the incidentangle of the light incident onto the optical waveplate 600 (i.e., inputlight) when the LC cell 104 is switched on to be at the homeotropicstate (e.g., V₂=10V). In the simulations, the optical waveplate 600 isconfigured to provide a 90° retardance when the LC cell 104 is switchedoff to be in the splay state (V₀=0V) and to provide a −90° retardancewhen the LC cell 104 is switched on to be at the homeotropic state(e.g., V₂=10V). The light incident onto the optical waveplate 600 ispresumed to be a linearly polarized light, and an angle between thepolarization direction of the light and the alignment direction of theLC cell 104 is presumed to be about 45°. In some embodiments, the lightincident onto the optical waveplate 600 may be linearly polarized in they-axis direction shown in FIG. 6.

As shown in FIG. 8, the vertical axis is the phase retardance providedby the optical waveplate 600, and the horizontal axis is the wavelength(in nm) of the light incident onto the optical waveplate 600. When theLC cell 104 is at a voltage-off state, the optical waveplate 600 mayprovide a phase retardance of about 90° for a broadband light (e.g., apolychromatic light) over a range of wavelengths, e.g. a range fromabout 400 nm to about 700 nm. When the LC cell 104 is at a voltage-onstate and a homeotropic state (e.g., V₂=10V), the optical waveplate 600may provide a phase retardance of about −90° for the broadband light.That is, at each of the voltage-on (or switch-on) and voltage-off (orswitch-off) states of the LC cell 104, the optical waveplate 600 mayprovide a predetermined phase retardance (e.g., a phase retardance ofabout 90° at the voltage-on state, or a phase retardance of about −90°at the voltage-off state) to a broadband light (e.g., a polychromaticlight) over a range of wavelengths, e.g. a range from about 400 nm toabout 700 nm, where the predetermined phase retardances may besubstantially wavelength independent over the range of wavelengths.

As shown in FIG. 9, the vertical axis is the phase retardance providedby the optical waveplate 600, and the horizontal axis is the incidentangle of the light incident on the optical waveplate 600. When the LCcell 104 is at the voltage-off state, the optical waveplate 600 mayprovide a phase retardance of about 90° to about 95° for lights with anincident angle in a range of about −45° to about 45°. When the LC cell104 is at the voltage-on state and at the homeotropic state (e.g.,V₂=10V), the optical waveplate 600 may provide a phase retardance ofabout −90° to about −100° for lights with an incident angle in a rangeof about −40° to about 40°. That is, at each of the voltage-on andvoltage-off states of the LC cell 104, the optical waveplate 600 mayprovide a phase retardance close to a predetermined, theoreticalretardance (e.g., close to 90° or −90°), to a broadband light (e.g., apolychromatic light) over a range of incident angles, e.g. a range fromabout −45° to about 45°.

As shown in FIG. 10, the horizontal axis is the incident angle of theinput light, and the vertical axis is the Stokes parameter S3 of theoutput light of the optical waveplate 600. The incident angle dependentStokes parameter S3 is evaluated at wavelengths of 460 nm, 530 nm, and620 nm, respectively. FIG. 10 shows that, when the LC cell 104 is at thevoltage-off state, at wavelengths of 460 nm, 530 nm, and 620 nm, for awide range of incident angles (e.g., about −40° to about 35°), theStokes parameter S3 of the output light may remain at or above 0.9,which is close to 1.0 (the theoretical value).

A person having ordinary skills in the art can understand that theright-handed circularly polarized light has the Stokes parameter S3=1.0,and the closer the Stokes parameter S3 approaches 1.0, the closer theoutput light approaches a right-handed circularly polarized light. Thus,according to FIG. 10, for a wide range of incident angles andwavelengths, the output light of the optical waveplate 600 when the LCcell 104 is switched off may be a right-handed circularly polarizedoutput light (S3=1.0) or a substantially right-handed circularlypolarized output light (S3≈1.0, e.g., S3≥0.9). That is, the opticalwaveplate 600 may convert the linearly polarized incident light to aright-handed circularly polarized output light or a substantiallyright-handed circularly polarized output light over a wide range ofincident angles and wavelengths. In other words, when the LC cell 104 isat the voltage-off state and at the splay state, the optical waveplate600 may have the broadband and large viewing angle performance.

As shown in FIG. 11, the horizontal axis is the incident angle of theinput light, and the vertical axis is the Stokes parameter S3 of theoutput light. The incident angle dependent Stokes parameter S3 isevaluated at wavelengths of 460 nm, 530 nm, and 620 nm, respectively. Asshown in FIG. 11, when the LC cell 104 is at the voltage-on state and atthe homeotropic state, at wavelengths of 460 nm and 530 nm, for a widerange of incident angles (e.g., about −40° to about 40°), the Stokesparameter S3 of the output light may remain at or below about −0.9,which is close to −1.0. At the wavelength of 620 nm, for a wide range ofincident angles (e.g., about −40° to about 40°), the Stokes parameter S3of the output light may remain at or below about −0.8.

A person having ordinary skills in the art can understand that theleft-handed circularly polarized light has the Stokes parameter S3=−1.0,and the closer the Stokes parameter S3 approaches −1.0, the closer theoutput light approaches a left-handed circularly polarized light. Thus,according to FIG. 11, for a wide range of incident angles andwavelengths, the output light of the optical waveplate 100 when the LCcell 104 is switched on to be at the homeotropic state may be aleft-handed circularly polarized output light (S3=−1.0) or asubstantially left-handed circularly polarized output light (S3≈−1.0).That is, when the LC cell 104 is at the voltage-on state and at thehomeotropic state, the optical waveplate 100 may convert the linearlypolarized incident light to a left-handed circularly polarized outputlight or a substantially left-handed circularly polarized output lightover a wide range of incident angles and wavelengths. In other words,when the LC cell 104 is at the voltage-on state and at the homeotropicstate, the optical waveplate 600 may have excellent broadband and largeviewing angle performance.

In some embodiments, the optical waveplate may include an active LC cell(e.g., only one active LC cell) that is controllable by an externalelectric field to switch between different states, while thecompensation films may be passive elements. For example, the LC cell maybe configured to switch between the splay state (e.g., V₀=0V) and thehomeotropic state (e.g., V₂=10V) rather than being switched between thebend state (e.g., V₁=2V) and the homeotropic state (e.g., V₂=10V) inconventional LC cells. Thus, a driving voltage may be applied only tothe LC cell 104 at the homeotropic state (e.g., V₂=10V). Accordingly,the power consumption of the optical waveplate may be reduced.

Further, the compensation films together may be configured to provide amajority portion of the retardance of the optical waveplate. That is, ina total retardance provided by the optical waveplate for a linearlyincident light, the three compensation films together may provide alarger portion of the total retardance than the LC cell. For example,the compensation films together may provide a larger than about 95%,90%, 85%, 80%, 75%, 70%, 65%, or 60% of the total retardance and,accordingly, the LC cell may provide smaller than about 5%, 10%, 15%,20%, 25%, 30%, 35% or 40% of the total retardance. Through configuringthe compensation films together to provide more than half (50%) of theretardance of the optical waveplate, the cell gap of the LC cell may beconfigured to be substantially small, which may reduce the drivingvoltage for the homeotropic state and the relaxing time transitioningfrom the homeotropic state to the splay state.

When the cell gap of the LC cell is substantially small, stronganchoring may occur at the surfaces of the alignment layers, resultingin the splay state of the LC cell being a stable state. Thus, when theLC cell is switched between the splay state under a zero voltage and thehomeotropic state under a relatively high voltage (e.g., V₂=10V), thetransition from the homeotropic state to the splay state after removingthe applied voltage may still be substantially fast due to the reducedbackflow effect in the Pi-cell. In contrast, when the cell gap issubstantially large, the bend state of the LC cell may become the stablestate after removing the applied voltage. As a result, when the LC cellrelaxes from the homeotropic state to the splay state after removing theapplied voltage, the transition from the bend state to the splay statemay take a long time, for example, several seconds. In some embodiments,the thickness of the LC cell in the disclosed optical waveguide may beconfigured to be about 1-1.5 μm. According to the present disclosure,the disclosed optical waveplate may have a reduced switching time and animproved spectral and angular performance as compared to a conventionalbroadband and wide-viewing-angle waveplate using TNLC cells.

In some embodiments, the compensation films (e.g., the positive-C film,the positive-A film, the negative biaxial retardation film) and the LCcell in the optical waveplate may be made of the same LC material and,thus, may have the same birefringence property. Any change intemperature that consequently changes the refractive index of the LCmaterial may be identical for the LC cell and the compensation films,such that the LC cell and the compensation films may self-compensateeach other for a large range of temperature variation. Accordingly, thetemperature stability and reliability of the optical waveplate may beimproved.

In some embodiments, the disclosed optical waveplate may include morethan one active cell (e.g., more than one LC cell). The more than one LCcell may be combined with one or more compensation films, such as one ormore negative biaxial retardation films, one or more positive-A films,one or more positive-C films. The number of compensation films may bedetermined based on the number of active cells and the opticalproperties to be achieved in the optical waveplate. In some embodiments,the optical waveplate may include multiple sets of the combination shownin FIG. 1 stacked together. For example, two sets of the combinationshown in FIG. 1 may be stacked together to form the optical waveplate.

The disclosed optical waveplates may have a large variety ofapplications in many instruments and optical systems, for example, anear-eye display (“NED”) for virtual-reality (“VR”), augmented-reality(“AR”), and/or mixed-reality (“MR”) applications. FIG. 12 illustrates aperspective view of an NED 1200 according to an embodiment of thepresent disclosure. FIG. 13 illustrates a cross-section 1250 of a frontbody of the NED 1200 shown in FIG. 12. The NED 1200 may include one ormore of the disclosed optical waveplates.

As shown in FIG. 12, the NED 1200 may include a front body 1205 and aband 1210. The front body 1205 may include one or more electronicdisplay elements of an electronic display (not shown), an inertialmeasurement unit (“IMU”) 1215, one or more position sensors 1220, andone or more locators 1225. In the embodiment shown by FIG. 12A, theposition sensors 1220 may be located within the IMU 1215, and neitherthe IMU 1215 nor the position sensors 1220 may be visible to the user.The NED 1200 may function as a VR, AR, and/or MR device, or somecombinations thereof. When the NED 1200 functions as an AR and/or MRdevice, portions of the NED 1200 and its internal components may be atleast partially transparent.

As shown in FIG. 13, the front body 1205 may include an electronicdisplay 1255 and a varifocal block 1260 that together guide an imagelight to an exit pupil 1270. The exit pupil 1270 may be a location ofthe front body 1205 where an eye 1265 of a user is positioned. Inaddition, the NED 1200 may include an eye-tracking system (not shown).The NED 1200 may present electronic content via the electronic display1255 to the user of the NED 1200 at a focal distance. The varifocalblock 1260 may be configured to adjust the focal distance in accordancewith instructions from the NED 1200 to, e.g., mitigate vergenceaccommodation conflict of eyes of the user. The focal distance may beadjusted by adjusting an optical power associated with the varifocalblock 1260, and specifically by adjusting the optical power associatedwith one or more optical lenses in the varifocal block 1260.

FIG. 14 illustrates a schematic diagram of a varifocal block 1460according to an embodiment of the present disclosure. The varifocalblock 1460 may be an embodiment of the varifocal block 1260 shown inFIG. 13. In some embodiments, the varifocal block 1460 may include oneor more Pancharatnam Berry Phase (“PBP”) liquid crystal (“LC”) lenses1461 (e.g., 1461-1, 1461-2, and 1461-3), one or more quarter-wave plate1462 (e.g., 1462-1 and 1462-2), and one or more switchable opticalwaveplate 1463 (e.g., 1463-1 and 1463-2) alternately arranged. Forexample, FIG. 14 shows three PBP LC lenses 1461-1, 1461-2, and 1461-3,two quarter-wave plates 1462-1 and 1462-2, and two switchable opticalwaveplates 1463-1 and 1463-2. The number of these optical elements arefor illustrative purposes only, and may be any suitable numbers. Alongthe light path (e.g., from the input light to the output light), a firstPBP LC lens 1461-1 may be disposed upstream of a first quarter-waveplate 1462-1, which may be disposed upstream of a first switchableoptical waveplate 1463-1. The first switchable optical waveplate 1463-1may be disposed upstream of a second PBP LC lens 1461-2, which may bedisposed upstream of a second quarter-wave plate 1462-2. The secondquarter-wave plate 1462-2 may be disposed upstream of a second opticalwaveplate 1463-2. A third PBP LC lens 1461-3 may be disposed downstreamof the second optical waveplate 1463-2. This configuration may berepeated along the light path for additional times. In some embodiments,a PBP LC lens 1461 (e.g., 1461-1, 1461-2, or 1461-3) may be operated inan additive state or a focusing state (which may add an optical power tothe varifocal block 1460) when receiving a right-handed circularlypolarized (“RHCP”) light. In some embodiments, a PBP LC lens 1461 may beoperated in a subtractive state or a defocusing state (which maysubtract an optical power from the varifocal block 1460) when receivinga left-handed circularly polarized (“LHCP”) light. The PBB LC lens 1461may reverse the handedness of the circularly polarized light transmittedtherethrough in addition to focusing and/or defocusing the circularlypolarized light.

A quarter-wave plate 1462 (e.g., 1462-1 or 1462-2) may convert thecircularly polarized light transmitted through an upstream PBP LC lens1461 to a linearly polarized light. A switchable optical waveplate 1463(e.g., 1463-1 or 1463-2) may have a polarization axis orientatedrelative to the polarization direction of the linearly polarized lightto convert the linearly polarized light to a left-handed circularlypolarized (“LHCP”) light or a right-handed circularly polarized (“RHCP”)light in accordance with a switching state of the optical waveplate1463. In some embodiments, the switchable optical waveplate 1463 may bean embodiment of the disclosed optical waveplate, such as the opticalwaveplate 600 shown in FIG. 6. For example, when the LC cell is switchedoff and switched on, the switchable optical waveplate 1463 mayrespectively provide a retardance of about 90° and about −90° for abroadband light (e.g., a polychromic light) covering a range ofwavelengths from 400 nm to 700 nm. Accordingly, when the LC cell isswitched off and switched on, the switchable optical waveplate 1463 mayconvert the linearly polarized light to an RHCP light and an LHCP light,respectively. In other words, the switchable optical waveplate 1463 mayoutput an RHCP or an RHCP light in accordance with a switching state ofthe optical waveplate 1463, i.e., a switching state (e.g., a voltage-onstate or a voltage-off state) of the LC cell in the switchable opticalwaveplate 1463. Thus, the first switchable optical waveplate 1463-1placed upstream of a second PBP LC lens 1461-2 in a path of an incidentlight may be configured to control whether the second PBP LC lens 1461-2functions in an additive state or in a subtractive state by controllingthe handedness of the circularly polarized light incident onto thesecond PBP LC lens 1461-2. Likewise, the second switchable opticalwaveplate 1463-2 placed upstream of a third PBP LC lens 1461-3 in a pathof an incident light may be configured to control whether the third PBPLC lens 1461-3 functions in an additive state or in a subtractive stateby controlling the handedness of the circularly polarized light incidentonto the third PBP LC lens 1461-3. Accordingly, the varifocal block 1460may provide a range of adjustment of optical powers to adapt for humaneye vergence-accommodation.

Because the disclosed optical waveplate has broadband performance, alarge acceptance angle, a low residual retardance, a fast response, anda capability of being switched between different states of retardances,the varifocal block 1460 may be configured to provide various opticalpowers to adapt for human eye vergence-accommodation in a fast andaccurate fashion over a wide range of incident angles and a wide rangeof incident wavelengths. The configuration of the varifocal blockincluding the stacked PBP LC lens structure shown in FIG. 14 is merelyfor illustrative purposes, and other configurations of the varifocalblock may be used according to various application scenarios.

The above-mentioned applications of the disclosed optical waveplates inthe NEDs are merely for illustrative purposes. In addition, thedisclosed optical waveplates may also be used to realize eye-trackingcomponents, display resolution enhancement components (e.g., increasingpixel density), and pupil steering elements, etc., in a large variety ofdevices and systems. The disclosed optical waveplates have a broadbandperformance for lights with wavelengths ranging from a visible region toa near infrared region, a large acceptance angle (e.g., a large incidentangle), a low residual retardance, a fast response, and a capability ofbeing switched between, for example, a zero retardance value and anon-zero retardance value. Thus, the optical waveplates may beimplemented as multifunctional optical components in the NEDs tosignificantly improve the optical performance of the NEDs.

The foregoing description of the embodiments of the disclosure have beenpresented for the purpose of illustration. It is not intended to beexhaustive or to limit the disclosure to the precise forms disclosed.Persons skilled in the relevant art can appreciate that manymodifications and variations are possible in light of the abovedisclosure.

Some portions of this description may describe the embodiments of thedisclosure in terms of algorithms and symbolic representations ofoperations on information. These operations, while describedfunctionally, computationally, or logically, may be implemented bycomputer programs or equivalent electrical circuits, microcode, or thelike. Furthermore, it has also proven convenient at times, to refer tothese arrangements of operations as modules, without loss of generality.The described operations and their associated modules may be embodied insoftware, firmware, hardware, or any combinations thereof.

Any of the steps, operations, or processes described herein may beperformed or implemented with one or more hardware and/or softwaremodules, alone or in combination with other devices. In one embodiment,a software module is implemented with a computer program productincluding a computer-readable medium containing computer program code,which can be executed by a computer processor for performing any or allof the steps, operations, or processes described. In some embodiments, ahardware module may include hardware components such as a device, asystem, an optical element, a controller, an electrical circuit, a logicgate, etc.

Embodiments of the disclosure may also relate to an apparatus forperforming the operations herein. This apparatus may be speciallyconstructed for the specific purposes, and/or it may include ageneral-purpose computing device selectively activated or reconfiguredby a computer program stored in the computer. Such a computer programmay be stored in a non-transitory, tangible computer readable storagemedium, or any type of media suitable for storing electronicinstructions, which may be coupled to a computer system bus. Thenon-transitory computer-readable storage medium can be any medium thatcan store program codes, for example, a magnetic disk, an optical disk,a read-only memory (“ROM”), or a random access memory (“RAM”), anElectrically Programmable read only memory (“EPROM”), an ElectricallyErasable Programmable read only memory (“EEPROM”), a register, a harddisk, a solid-state disk drive, a smart media card (“SMC”), a securedigital card (“SD”), a flash card, etc. Furthermore, any computingsystems described in the specification may include a single processor ormay be architectures employing multiple processors for increasedcomputing capability. The processor may be a central processing unit(“CPU”), a graphics processing unit (“GPU”), or any processing deviceconfigured to process data and/or performing computation based on data.The processor may include both software and hardware components. Forexample, the processor may include a hardware component, such as anapplication-specific integrated circuit (“ASIC”), a programmable logicdevice (“PLD”), or a combination thereof. The PLD may be a complexprogrammable logic device (“CPLD”), a field-programmable gate array(“FPGA”), etc.

Embodiments of the disclosure may also relate to a product that isproduced by a computing process described herein. Such a product mayinclude information resulting from a computing process, where theinformation is stored on a non-transitory, tangible computer readablestorage medium and may include any embodiment of a computer programproduct or other data combination described herein.

Further, when an embodiment illustrated in a drawing shows a singleelement, it is understood that the embodiment may include a plurality ofsuch elements. Likewise, when an embodiment illustrated in a drawingshows a plurality of such elements, it is understood that the embodimentmay include only one such element. The number of elements illustrated inthe drawing is for illustration purposes only, and should not beconstrued as limiting the scope of the embodiment. Moreover, unlessotherwise noted, the embodiments shown in the drawings are not mutuallyexclusive, and they may be combined in any suitable manner. For example,elements shown in one embodiment but not another embodiment maynevertheless be included in the other embodiment.

Various embodiments have been described to illustrate the exemplaryimplementations. Based on the disclosed embodiments, a person havingordinary skills in the art may make various other changes,modifications, rearrangements, and substitutions without departing fromthe scope of the present disclosure. Thus, while the present disclosurehas been described in detail with reference to the above embodiments,the present disclosure is not limited to the above describedembodiments. The present disclosure may be embodied in other equivalentforms without departing from the scope of the present disclosure. Thescope of the present disclosure is defined in the appended claims.

What is claimed is:
 1. An optical waveplate, comprising: a positive-Cfilm including a first liquid crystal (“LC”) layer, tilt angles of LCmolecules in the first LC layer varying along a thickness direction ofthe first LC layer; an LC cell disposed at a first side of thepositive-C film and including a second LC layer aligned in an opticallycompensated bend (“OCB”) mode; a positive-A film disposed at a secondside of the positive-C film; and a negative biaxial retardation filmdisposed between the positive-A film and the positive-C film, whereinthe LC cell is switchable between at least two predetermined states. 2.The optical waveplate according to claim 1, wherein the at least twopredetermined states of the LC cell include a splay state and ahomeotropic state.
 3. The optical waveplate according to claim 1,wherein the first LC layer is a nematic LC layer.
 4. The opticalwaveplate according to claim 3, wherein along the thickness direction ofthe first LC layer, absolute values of the tilt angles of the LCmolecules in the first LC layer gradually increase from each of twoedges of the first LC layer to a center portion of the first LC layer.5. The optical waveplate according to claim 4, wherein the absolutevalues of the tilt angles of the LC molecules at each of the two edgesof the first LC layer are in a range of about 0° to about 5°, and theabsolute values of the tilt angles of the LC molecules at the centerportion of the first LC layer are in a range of about 88° to about 90°.6. The optical waveplate according to claim 4, wherein the two edges ofthe first LC layer are a first edge and a second edge, the tilt anglesof the LC molecules gradually increase from about +3° at the first edgeto about +90° at the center portion, the tilt angles of the LC moleculesgradually increase from about −3° at the second edge to about −90° atthe center portion, and the tilt angles of the LC molecules abruptlychanges from about +90° to about −90° at the center portion.
 7. Theoptical waveplate according to claim 1, wherein the optical waveplate isconfigured to provide an amount of phase retardance to an incidentlight, and the positive-C film, the positive-A film, and the negativebiaxial retardation film together providing more than half of the amountof the phase retardance to the incident light.
 8. The optical waveplateaccording to claim 7, wherein the positive-A film and the negativebiaxial retardation film together provide greater than or equal to about60% of the amount of the phase retardance to the incident light.
 9. Theoptical waveplate according to claim 1, wherein the optical waveplate isconfigured to provide an amount of phase retardance to lights in apredetermined range of wavelengths and a predetermined range of incidentangles, and the positive-C film, the positive-A film, the negativebiaxial retardation film, and the LC cell are oriented relative to eachother in a predetermined configuration to provide the amount of phaseretardance substantially independent of the wavelengths in thepredetermined range of wavelengths, and substantially independent of theincident angles in the predetermined range of incident angles.
 10. Theoptical waveplate according to claim 1, wherein the positive-C film hasn_(x)=n_(y)<n_(z), the positive-A film has n_(x)>n_(y)=n_(z), and thenegative biaxial retardation film has n_(x)>n_(y)>n_(z), n_(x) and n_(y)being principal refractive indices in orthogonal x and y directions at afilm plane, and n_(z) being a principal refractive index in a thicknessdirection perpendicular to the film plane.
 11. The optical waveplateaccording to claim 1, wherein an alignment direction of the LC cell isorientated at about −35° to about −50° relative to a predetermineddirection, a fast axis of the positive-C film is orientated at about 35°to about 50° relative to the predetermined direction, a slow axis of thenegative biaxial retardation film is orientated at about −35° to about−50° relative to the predetermined direction, and a slow axis of thepositive-A film is orientated at about 35° to about 50° relative to thepredetermined direction.
 12. The optical waveplate according to claim11, wherein the alignment direction of the LC cell is orientated atabout −45° relative to the predetermined direction, the fast axis of thepositive-C film is orientated at about 45° relative to the predetermineddirection, the slow axis of the negative biaxial retardation film isorientated at about −45° relative to the predetermined direction, andthe slow axis of the positive-A film is orientated at about 45° relativeto the predetermined direction.
 13. The optical waveplate according toclaim 11, wherein the predetermined direction is along a polarizationdirection of a linearly polarized incident light.
 14. The opticalwaveplate according to claim 1, wherein the LC cell has a cell gap ofabout 1 to about 1.5 μm.
 15. The optical waveplate according to claim 1,wherein the LC cell, the positive-C film, the negative biaxialretardation film and the positive-A film are sequentially disposed in apath of an incident light.
 16. The optical waveplate according to claim1, wherein the positive-C film, the positive-A film, the negativebiaxial retardation film, and the LC cell include a same LC material.17. The optical waveplate according to claim 1, wherein the positive-Cfilm includes an LC material with a negative dielectric anisotropy.